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WASHINGTON (CNN) -- Support for the country's new health care law has dropped to a record low, according to a new national poll.

And a CNN/ORC International survey released Monday also indicates that most Americans predict that the Affordable Care Act will actually result in higher prices for their own medical care.

Only 35% of those questioned in the poll say they support the health care law, a 5-point drop in less than a month. Sixty-two percent say they oppose the law, up four points from November.

Nearly all of the newfound opposition is coming from women.

"Opposition to Obamacare rose six points among women, from 54% in November to 60% now, while opinion of the new law remained virtually unchanged among men," CNN Polling Director Keating Holland said. "That's bad news for an administration that is reaching out to moms across the country in an effort to make Obamacare a success."

According to the survey, 43% say they oppose the health care law because it is too liberal, with 15% saying they give the measure a thumbs down because it is not liberal enough. That means half the public either favors Obamacare, or opposes it because it's not liberal enough, down four points from last month.

Sixty-three percent say they believe the new law will increase the amount of money they personally pay for medical care, which may not be a good sign for a law known as the "Affordable Care Act."

The survey also indicates that 42% say they will be personally worse off under Obamacare, with 16% saying the law will help them, and four in 10 saying it will have no effect on them.

Just over six in 10 say they believe they will be able to receive care from the same doctors that they now use, with 35% saying they will not be able to see the same doctors.

The Affordable Care Act, which is the signature domestic achievement for President Barack Obama, was passed along party lines in 2010, when Democrats controlled both houses of Congress. Since that passage, Republicans have fought to either repeal, defund, or severely restrict the law. A push by congressional conservatives to defund the law was the catalyst for October's 16-day long partial federal government shutdown, the first in nearly two decades.

The roll out of the law was extremely flawed, from the rocky startup of HealthCare.gov in October to the controversy over millions of Americans being told they would lose their current insurance plans because they didn't meet standards mandated by the new health care law.

Despite all the problems, the President said things are starting to improve, adding that more than 500,000 Americans enrolled in the Affordable Care Act through HealthCare.gov during the first three weeks of December.

"So all told, millions of Americans, despite problems with the website, are now poised to be covered by quality affordable health care," he said at a news conference.

The poll was conducted for CNN by ORC International December 16-19, with 1,035 adults nationwide questioned by telephone. The survey's overall sampling error is plus or minus three percentage points.